Notation Definition and 1000 Threads

Hello everyone! I came across, in a reading, an unfamiliar norm notation: $||A-B||_{2,a}$ where $a$ is the standard deviation of a Gaussian kernel. Now I know that the index 2 represents the $\ell _2$ norm, but what about the $a$? Moreover, is the matrix norm defnied in a similar way to the...

Homework Statement I'm trying to grasp how the indices are listed when writing out multiple vector products or divergences or gradients, etc. I'm working with 'An Introduction to General Relativity' by Hughston and Tod.Homework Equations A\wedge B = \varepsilon_{ijk}A_{j}B_{k} [A,B,C] =...

Homework Statement According to the question, i have to convert 3.60 * 105 to regular notation, without changing the number of significant figures, which is currently, as i understand, three. I'm just really unsure how to do this. Any help? Homework Equations Some said to write out...

Hi all, I don't know if analysis is the right place for me to post this thread therefore please accept my apologies in advance if I am mistaken. In graph theory the incidence function that associates vertices & edges http://img41.imageshack.us/img41/8171/32004284.jpg , in the text it has...

I wrote a program that writes arrays in a namelist under MinGW in Win7. The array is 100x2. It is written in two columns, alf(*,1) and then alf(*,2), where * means 100 row elements. It puts out the name of the array followed by a lot of numbers without any alf(1,1), alf(2,1), ..., alf(1,100)...

In some places I see that poisson bracket of {q_{i},p_{j}} = 1 (if i=j) and other times I see that this same bracket equals to -1. This is very confusing! What to do?

2A\mu=-\muoJ\mu Griffith's Introduction to Electrodynamics refers to this 4-vector equation as "the most elegant (and the simplest) formulation of Maxwell's equations." But does this encapsulate the homogeneous Maxwell Equations? I see how the temporal components lead to Gauss' Law, and I'm...

Homework Statement What does this notation mean? I understand the $$\{x_t\}_{t = 0}^{\infty}$$ part, but I don't know what exactly $$U(x_0, x_1, ... x_n)$$ means. Does it mean that this function is a n+1 dimensional function, the same way f(x, y) is a 3 dimensional function? Homework Equations...

Every paper I read about cross-section measurements from colliders has a line saying (for example): ...positron-electron annihilations at \sqrt{s} = 40 GeV are studied... 1) What does this mean? I'm guessing it means that in the CM frame, the energy of each beam is 40 GeV. 2) Why use...

The frequency, ω, of the source in the circuit of Figure 2 is adjusted until ig is in phase with vg. (a)using complex notation, determine the value of ω (rad/sec) Can anyone out there please help with this question? I've tried multiple methods but I am really struggling with simplifying the...

When you write vector quantities with unit vectors, do you still have to draw an arrow on top to indicate that it's a vector? e.g. velocity and acceleration. My textbook doesn't have it bolded so does that mean they're just taking the magnitude and then multiplying by the unit vector to make it...

This isn't a homework problem, but it's so simple that it belongs here. Can someone please explain to me bra and ket notation? I've been consulting various books and they are all so abstract. Yesterday, my professor told me that a ket |ψ> represents a column matrix and a bra <ψ| represents a...

Hello world, Index notation is driving me crazy: why on Earth is ∂_i 1/r = -x_i/r^3 ? I would expect it to be -x_i/r^2... Thanks for commenting

Hi. I'm asked to convert 2 year into the SI Unit seconds: Known: 1 Hr = 3600 s 1 Day = 86400 s So using a calculator... 1 yr = 365*86,400 = 31,536,000 I want to express the answer in scientific notation: Because the lesser number on has 3 significant digits, the scientific...

If an example was written; h(x) = 1/x and the function h has domain R excluding 0, could somebody please explain how the two open intervals include (- infinity, 0) and (0, infinity)? (Headbang)

Why is it that when you are doing a partial derivative it is expressed something like this. ∂f/∂x=2xy, where f(x,y)=x2y but when doing double or triple integrals you see this ∫∫f(x,y)dxdy. Why is partial notation not used in both?

Dear Physics Forums Community, I am reading "Theory of Probability and Random Process" by Koralov L.B. and Sinai Y.G. and am having a hard time trying to understand the notation shown below (page 10). In particular, what does ω:ε(w)=x mean below the second summation? And how the authors...

So I know that the Hodge dual of a p-form A_{\mu_1 \mu_2\cdot \cdot \cdot \mu_p} in d dimensions is given by (*A)^{\nu_1 \nu_2 \cdot \cdot \cdot \nu_{d-p}} = C\epsilon^{\nu_1 \nu_2 \cdot \cdot \cdot \nu_{d-p}\mu_1 \mu_2 \cdot \cdot \cdot \mu_p}A_{\mu_1 \mu_2\cdot \cdot \cdot \mu_p} where C...

I'm working on a project that required me to go through the literature to find some information on Compton and Rayleigh scattering. I came across a key expression, part of it which read: max{ f(x,Z), g(x,Z) } if Z > 10 and f(x,Z) < 2 where f(x,Z) and g(x,Z) are known functions. The...

Homework Statement The frequency, ω, of the source in the circuit of Figure 2 is adjusted until ig is in phase with vg. (a)using complex notation, determine the value of ω (rad/sec) (b)if vg = 20 sin ω t [where ω is the frequency found in 2(a)], determine an expression for the output...

Homework Statement 1 (a) using complex notation, find an expression for the output voltage, v0 1 (b) using complex notation, find an expression for the input current, ig, and hence determine the phase angle of ig relative to vg Homework Equations The Attempt at a Solution...

I am confused about the the notation |ab> for an entangled pair. Isn't this the same as the tensor product |a> \otimes |b>? If so, I run into another confusion when using the corresponding matrices. I read that I should apply a Hadamard operator H twice to the input state |01>. Does this mean...

\{\vec{A},\vec{B}\}\cdot \vec{C}=\vec{A}(\vec{B}\cdot \vec{C}) \vec{C} \cdot \{\vec{A},\vec{B}\}=(\vec{C}\cdot \vec{A}) \vec{B} I want to write dyade in Dirac notation. (|\vec{A}\rangle\langle\vec{B}|)|\vec{C}\rangle= |\vec{A}\rangle\langle\vec{B}|\vec{C}\rangle...

Homework Statement So originally Ag core notation should be -> Kr 5s1 4d10... but looking at it unchanged is -> Kr 5s2 4d9 Does that mean if i take an electron away I take away all the electrons from 5s2 and put them into the 4d8 shell and have Kr 4d10? Homework Equations The...

Homework Statement A series L-R-C circuit consisting of a voltage source, a capacitor of capacitance , an inductor of inductance , and a resistor of resistance is driven with an AC voltage of amplitude and frequency . Define to be the amplitude of the voltage across the resistor and the...

First of all, I'd like to say hi to all the peole here on the forum! Now to my question: When reading some general relativity articles, I came upon this strange notation: T^{a}_{b} = C(dt)^{a}(∂_{t})_{b} + D(∂_{t})^{a}(dt)_{b}. Can someone please explain to me what this means? Clearly...

Is the following the definition of wedge product in tensor notation? Let A \equiv A_i be a matrix one form. Then A \wedge A \wedge A \wedge A \wedge A = \epsilon^{abcde}A_a A_b A_c A_d A_e ? in 5 dimensions. This question is in reference to the winding number of maps.

hi all, i have codes for 1d fdtd maxwell equation. the problem i am facing right now is some error regarding the kind notation. !1d fdtd Simulation in free space subroutine fd1d01(f0,miu,delta,S,E0) implicit none real :: f0 real :: miu real :: delta real...

Hello all, Homework Statement I’m trying to derive a result from a book on quantum mechanics but I have trouble with bra-ket notation and operators… Let’s say we have a photon moving along the cartesian z-axis. It is polarized and its state is Psi(theta) = cos (theta) x1 + sin(theta) x1...

I don't know how to properly present my answer to find the limit of a converging sequence like (1/2)^n. I would just write something like this... y=1/x+1, x=∞ } y=1/∞+1=0+1=1 but the syllabus gives something completely different and my textbooks don't seem to cover this portion of the...

Homework Statement What is happening from the green box to the blue box? I am completely lost as to what this example is trying to show. Would really appreciate some info on this, thanks. Homework Equations

If x,y,z are the position operators. Is it true that: <φ|x|φ> + <φ|y|φ> + <φ|z|φ> = <φ | x+y+z| φ> ? So that if, for example, one wanted to compute <φ|r|φ> (where r =x+y+z), then they would just have to sum the parts. I know that for scalars, a and b, we have the following...

Does anyone know how to do box notation in Latex, I've got this: Li \quad \boxed{\uparrow \downarrow} \quad \boxed{\uparrow\;} \qquad 1s 2s But I want the quantum states to appear underneath their respective boxes?

Homework Statement I'm actually asked to calculate the area under the curve 5x + x2 over the interval [0,1] using Riemann Sums. I found the formula for the Riemann sum over the interval, it being the following: \sum^{n}_{k=1} (\frac{5k}{n}+\frac{k^{2}}{n^{2}})(\frac{1}{n}) However, I...

Homework Statement Find <P>. P = i√(mhw/2)(a†-a). Note a† and a are the ladder operators. P is the momentum operator of the harmonic oscillator. |ψ > = (1/sqrt(2))[ |1> - i |2>] The answer should be zero, can someone check my work?Homework Equations a† |n> = sqrt(n+1)|n+1> a |n> =...

Homework Statement "Express the following sum in sigma notation: 1 + (2/3) + (3/5) + (4/7) + (5/9)" Homework Equations The Attempt at a Solution I've figured out what they all have in common (1+2=3, 2+3=5, 3+4=7, 4+5=9) but I've been searching through the book and on the...

Homework Statement The problem regards a ball thrown vertically, there is a model of the motion that we worked out, from the original equation a(t) = -(g/b^2)(v^2+b^2) With some help from another forum member I integrated with regard to t (dv/dt?) this to...

Hi Pf, Here is a question regard a test review that we have. I am not looking for the answer but rather a clarification about the notation. 1. What does the following mean? T1: \Re2 \rightarrow \Re2 by x \rightarrow Ax? 2. What does it mean to go \Re2 \rightarrow \Re2 Thanks.

in the appendix on Group Theory in Zee's book there is a discussion of commutations for SO(3) two questions - does [J^{ij},J^{lk}] = J^{ij}*J^{lk}-J^{lk}*J^{ij}? and there is an expression in the appendix that the commutator equals i(\delta^{ik}J^{jl} ... i don't understand the why...

Hello everyone! Now this may seem silly to you, but I'm rather interested in syntax on this one: $\displaystyle \int _a ^b f(x)dx= - \int _b ^a f(x)dx$, but $\displaystyle \Sigma_{n=A} ^B = \Sigma_{n=B} ^A$ i.e. there is no need for a minus sign, is this generally accepted in terms of syntax...

Homework Statement Hi Whenever I read about the dipole approximation in QM, then the Hamiltonian is given as \hat {V}_{\text{dipole}} = -\mathbf{d}\cdot \mathbf{E} where E is the electric field and d the dipole operator. What I am wondering about is that d is an operator. Is it wrong to...

Hello. I'm trying to grasp the notation for the definition of something called the weak q-norm, defined as \|x\|_{q,w}^q = \sup\limits_{\epsilon > 0} \epsilon^q \left| \Big\{i \,|\, |x_i| > \epsilon \Big\} \right| I don't come from a pure math background so I've never seen this...

Homework Statement [A^{+}A]=1 A|a>=\sqrt{a}|a-1> A^{+}|a>=\sqrt{a+1}|a+1> <a'|a>=\delta_{a'}_{a} Homework Equations what is 1 <a|A|a+1> 4. <a+1|A^{+}|a> 3. <a|A^{+}A|a> 4. <a|AA^{+}|a> The Attempt at a Solution 1. <a|A|a+1> =<a|\sqrt{a+1}|a+1-1>=\sqrt{a+1}<a|a> since a=a and...

Hey guys, I'm an engineering PhD student, and I'm doing some work with laser-induced fluorescence. At the moment, I'm trying to understand some notation about the excited states of nitrogen dioxide. One of the papers I'm looking at, V.M. Donnelly, et al. J. Chem. Phys. 71, 659 (1979), is saying...

Homework Statement http://desmond.imageshack.us/Himg100/scaled.php?server=100&filename=img20120327195119.jpg&res=medium Homework Equations The Attempt at a Solution I just plugged in ∞ for n [2+\frac{3}{∞}]2 (\frac{3}{∞}) = [2+0]2 (0) = 0Did I do the problem correctly? I might need a...

Hi Is it correct of me to say that I want to carry out the sum \sum_i{v_iw_i} where i\in\{x,y,z\}? Or is it most correct to say that i=\{x,y,z\}?Niles.

Spinor notation exercise with grassman numbers I'm checking a term when squaring a vector superfield in Wess-Zumino gauge, but its really just an excercise in index/spinor notation: I need to square the term...

Hello, I am looking at a derivation that involves (note x is a column vector) \frac {d(\vec{x}^T\vec{x})} {d\vec{x}} = \vec{x}^{T} So I convert to summation notation and evaluate as follows \sum_{i,j} \frac {d(x_{i}x^{i})} {dx^{j}} \sum_{i,j} \frac {dx_{i}} {dx^{j}} x^{i} + \sum_{i,j}...

what kind of math language is this? $I\subset \reals$ $$\gamma_i:I_i\rightarrow M,\quad I_i\subset\reals,\quad i=1,2$$ $\sigma_{\alpha\beta}$ , let $$\rJ\sigma_{\alpha\beta}:V_{\alpha\beta}\rightarrow \Mat_{n,n}(\reals)$$ I have seen this notation thrown around in this forum, but I never...

Hi All, So here's my question: Suppose we have two sets A and B, then A \setminus B denotes their set-difference. Does there exist an equivalent operator for the case where A and B are not sets, but sequences? Otherwise, is there an operator to convert a sequence into a set...